The effect of turbulent mixing in the reaction zone of a tubular low-density polyethylene reactor was studied by combining a Langrangian composition probability density function (LCPDF) code with a computational fluid-dynamics code. Because the LCPDF code can treat the chemical reaction terms in a turbulent flow without resorting to moment closures, it is used to describe the temperature and scalar fields of reactants including initiator and monomer molar concentrations, and the moments of the molecular weight distribution. The chemical reaction terms are efficiently dealt with using a three-parameter chemical lookup table that contains the temperature and composition changes as functions of initiator and monomer concentrations and temperature over a small time step. The reaction-rate constants from the study of Lee and Marano (1979) are functions of temperature and pressure. The flow fields are obtained using the k - epsilon turbulence model. Because the temporal and spatial evolution of all fields in the reactor can be simulated, it is possible to study the effect of the initiator injection location, flow rate and temperature of the monomer and initiator feed streams on polymerization in considerable detail. Moreover, by observing the probability distribution of the composition fields, a better understanding of hot-sot formation is achieved, leading to improved reactor designs.